Zhongkai Tao

I'm a graduate student at UC Berkeley. I am interested in microlocal analysis. My advisor is Maciej Zworski. My email is ztao@math.berkeley.edu. Here is my CV.

Research

  • Integral formulas for under/overdetermined partial differential operators via recovery on curves, with Philip Isett, Yuchen Mao and Sung-Jin Oh, in preparation;

  • Flexibility of maximal asymptotically flat initial data sets, with Yuchen Mao and Sung-Jin Oh, in preparation;

  • Selberg, Ihara and Berkovich, with Jialun Li, Carlos Matheus and Wenyu Pan, in preparation;

  • Dirac cones and magic angles in the Bistritzer--MacDonald TBG Hamiltonian, with Simon Becker, Solomon Quinn, Alexander Watson and Mengxuan Yang.

  • Spectral gap for surfaces of infinite volume with negative curvature.

  • Optimal enhanced dissipation for contact Anosov flows, with Maciej Zworski.

  • Appendix to Mathematical results on the chiral model of twisted bilayer graphene, with Mengxuan Yang, Journal of Spectral Theory, 14(2024), no.3, 1063–1107.

  • Appendix to Classically forbidden regions in the chiral model of twisted bilayer graphene, with Maciej Zworski.

  • Initial data gluing in the asymptotically flat regime via solution operators with prescribed support properties, with Yuchen Mao and Sung-Jin Oh.

  • Counting Pollicott--Ruelle resonances for Axiom A flows, with Long Jin.

  • The fractal uncertainty principle via Dolgopyat's method in higher dimensions, with Aidan Backus and James Leng, to appear in Analysis&PDE.

  • Spectral asymptotics for kinetic Brownian motion on Riemannian manifolds, with Qiuyu Ren.

  • Localized initial data for Einstein equations, with Yuchen Mao.

  • Spectral asymptotics for kinetic Brownian motion on locally symmetric spaces, with Qiuyu Ren.

  • Flat trace estimates for Anosov flows, with Long Jin.

  • Exact control for Schrödinger equation on torus from small balls, Pure and Applied Analysis 3(2021), 387-401.

  • On 0-th order pseudodifferential operator on the circle, Proceedings of the AMS, 152(2024), no.8, 3289–3297.

    • Selected Talks

    Teaching

  • Fall 2024: Directed Reading Program with Jiaqi Hao on microlocal analysis.

  • Spring 2022: Directed Reading Program with Troy Tsubota on differentiable manifolds.

  • Fall 2021: Math 53 Multivariable Calculus.

  • Spring 2021: Math 53 Multivariable Calculus.

  • Fall 2020: Directed Reading Program with Ayush Kamat on measure theory.

    Notes

  • Notes on random perturbation of non-self-adjoint operators, taken from the topics course in Spring 2021 taught by Maciej Zworski.

    • Seminar

  • I organized a learning seminar on fractal uncartainty principle in January, 2022.

  • I organized a learning seminar on semiclassical analysis in spring 2022.

  • I co-organized Harmonic Analysis and Differential Equations Seminar (HADES) with Yonah Borns-Weil and Izak Oltman from fall 2022 to spring 2023.

  • I co-organized a learning seminar on orbit method for automorphic forms in fall 2023 with Christopher Dowd and Seewoo Lee.